Spectrally-resolved three-dimensional shape measurement device and spectrally-resolved three-dimensional shape measurement method

ABSTRACT

An apparatus includes: an interferometer configured to produce white light fringes with measuring light reflected or scattered by an object; an image sensor configured to generate an image signal for each pixel; and a controller. The interferometer splits the measuring light into two luminous fluxes and reflects them on reflecting mirrors having different curvatures. A white light fringe signal is obtained by varying the optical path difference between the two luminous fluxes. The controller is configured to perform frequency conversion on the white light fringe signal, with respect to the optical path difference, to determine a cross spectral density representing spectral information of each point on the object. The controller is configured to perform back-propagation computation based on Fresnel diffraction integral on the cross spectral density to determine a wavefront of light from each point on the object.

This nonprovisional application is based on Japanese Patent ApplicationNo. 2016-105606 filed on May 26, 2016 with the Japan Patent Office, theentire contents of which are hereby incorporated by reference.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to a spectrally-resolved three-dimensionalshape measurement device and a spectrally-resolved three-dimensionalshape measurement method to measure the three-dimensional shape and thespectral information of an object.

Description of the Background Art

A technique for measuring the three-dimensional shape and the spectralinformation of an object using white light interference hasconventionally been proposed. For example, a spectrally-resolvedthree-dimensional shape measurement device disclosed in Japanese PatentLaying-Open No. 2011-21991 includes an interferometer to produce whitelight fringes based on measuring light reflected or scattered by anobject illuminated with white light, a point detector to measure theintensity of light outputted from the interferometer, and a controllerconnected to the point detector to determine the three-dimensional shapeand the spectral information of the object from a white lightinterference signal. The interferometer splits the measuring light intotwo luminous fluxes. The controller produces three-dimensional whitelight fringes by varying the positional relationship between theinterferometer and the object and varying the optical path differencebetween the two luminous fluxes. The controller performs frequencyconversion on the three-dimensional white light fringes, with respect tothe optical path difference, to determine the cross spectral densityrepresenting the spectral information at a given point of the object.The controller performs frequency conversion on the cross spectraldensity, with respect to the movement amount of the interferometer, todetermine the wavefront of light from the given point on the object.

In the technique described in Naik et al. (“Spectrally resolvedincoherent holography: 3D spatial and spectral imaging using a MachZehnder radial-shearing interferometer”, OPTICS LETTERS, Optical Societyof America, Vol. 39, No. 7, pp. 1857-1860, 2014), light from an objectis guided into a Mach-Zehnder interferometer. An interference signal isacquired using an image sensor while a piezoelectric element is moving areflecting mirror disposed on one of the optical paths of theMach-Zehnder interferometer. The technique reproduces thethree-dimensional shape information and the spectral information of theobject from the interference signal.

In the technique described in Kim (“Full color natural light holographiccamera”, OPTICS EXPRESS, Optical Society of America, Vol. 21, Issue 8,pp. 9639-9642, 2013), light from an object is split into two luminousfluxes by a beam splitter. One of the luminous fluxes is reflected by aconcave mirror, while the other is reflected by a plane mirror. Thereflected luminous fluxes then pass through the beam splitter again tobe combined with each other. The combined luminous flux is imaged by aCCD camera having three color channels: red (R), green (G), and blue(B). In this technique, the CCD camera images the combined luminous fluxwhile the plane mirror is moved in the direction away from the beamsplitter, thus generating a plurality of images for each color channel.From the images obtained for each color channel, a hologram isregenerated for each color channel. The holograms are superimposed onone another to be a full-color hologram for the object.

In the technique disclosed in Japanese Patent Laying-Open No.2011-21991, during a measuring operation, a position of aninterferometer relative to an object is two-dimensionally moved toproduce interference fringes caused by interference between differentwavefront positions, so that the wavefront from each point on the objectis reproduced. The technique acquires interference fringes by varyingthe optical path difference between two luminous fluxes, so as toexamine the wavelength of light reflected or scattered at each point onthe object during the measuring operation. Specifically, during themeasuring operation, the technique moves the interferometer along eachof two axes orthogonal to each other, and further moves one of tworeflector elements, included in the interferometer, along one axis. Inthis technique, therefore, the measuring operation takes too much time.In particular, if the object is an object that changes over time (e.g. aliving body), the technique may not accurately measure thethree-dimensional shape or the spectral information of the object, dueto the change in the object during the measuring operation.

In the technique described in Naik et al., the optical path differencebetween two luminous fluxes is varied by moving a mirror disposed on oneof the optical paths of the Mach-Zehnder interferometer. The techniquetherefore involves a wavefront aberration. In order to measure thewavefront aberration, the technique brings laser light into theinterferometer separately from light from the object, senses the laserlight by the image sensor, and corrects the wavefront aberration basedon the sensing results. The technique, therefore, requires a complexoptical system for measuring white light fringes.

In the technique disclosed in Kim, in order to obtain the spectralinformation, one of the reflecting mirrors needs to be moved for eachcolor channel. Therefore, with the increase in the number of colorchannels for regenerating the wavefront of an object, a longer time isrequired for measuring the object.

SUMMARY OF THE INVENTION

In view of the above problems, an object of the present invention is toprovide a spectrally-resolved three-dimensional shape measurement deviceand a spectrally-resolved three-dimensional shape measurement methodcapable of measuring the three-dimensional shape and the spectralinformation of an object while reducing a time required for measuringthe object.

According to one embodiment of the present invention, aspectrally-resolved three-dimensional shape measurement device forobtaining a three-dimensional shape and spectral information of anobject is provided. The spectrally-resolved three-dimensional shapemeasurement device comprises: an interferometer configured to producewhite light fringes based on measuring light reflected or scattered bythe object illuminated with light having wavelengths; an image sensorconfigured to generate an image signal for each pixel, the image signalrepresenting an intensity distribution of light outputted from theinterferometer; and a controller connected to the image sensor andconfigured to determine the three-dimensional shape and the spectralinformation of the object from the image signal. The interferometerincludes: a beam splitting element configured to split the measuringlight into a first luminous flux and a second luminous flux; a firstreflecting mirror having the first reflection surface arranged forreflecting the first luminous flux to the beam splitting element, thefirst reflection surface having a first curvature; a second reflectingmirror having the second reflection surface arranged for reflecting thesecond luminous flux to the beam splitting element, the secondreflection surface having a second curvature different from the firstcurvature; and a movable stage configured to move the second reflectingmirror in a first direction parallel to a straight line that connectsthe beam splitting element and the second reflecting mirror to eachother, so as to change a distance between the beam splitting element andthe second reflecting mirror, thereby producing an optical pathdifference between the first luminous flux and the second luminous flux.The controller is configured to: acquire a white light fringe signalrepresented by a plurality of image signals generated by the imagesensor, while controlling the movable stage to move the secondreflecting mirror in the first direction; perform frequency conversionon the white light fringe signal, with respect to the optical pathdifference between the first luminous flux and the second luminous flux,so as to determine a cross spectral density representing spectralinformation of each point on the object; and perform back-propagationcomputation based on Fresnel diffraction integral on the cross spectraldensity, so as to determine a wavefront of light reflected or scatteredat each point on the object.

In the spectrally-resolved three-dimensional shape measurement device,both of the first reflecting mirror and the second reflecting mirror arepreferably concave mirrors.

According to another embodiment of the present invention, aspectrally-resolved three-dimensional shape measurement method adaptedfor a spectrally-resolved three-dimensional shape measurement device isprovided. The spectrally-resolved three-dimensional shape measurementdevice comprises: an interferometer configured to produce white lightfringes with measuring light reflected or scattered by an objectilluminated with light having wavelengths; and an image sensorconfigured to generate an image signal for each pixel, the image signalrepresenting an intensity distribution of light outputted from theinterferometer. The interferometer includes: a beam splitting elementconfigured to split the measuring light into a first luminous flux and asecond luminous flux; a first reflecting mirror having a reflectionsurface arranged for reflecting the first luminous flux to the beamsplitting element, the reflection surface having a first curvature; asecond reflecting mirror having a reflection surface arranged forreflecting the second luminous flux to the beam splitting element, thereflection surface having a second curvature different from the firstcurvature; and a movable stage configured to move the second reflectingmirror in a first direction parallel to a straight line that connectsthe beam splitting element and the second reflecting mirror to eachother, so as to change a distance between the beam splitting element andthe second reflecting mirror, thereby producing an optical pathdifference between the first luminous flux and the second luminous flux.The spectrally-resolved three-dimensional shape measurement methodcomprises: acquiring a white light fringe signal represented by aplurality of image signals generated by the image sensor, whilecontrolling the movable stage to move the second reflecting mirror inthe first direction; performing frequency conversion on the white lightfringe signal, with respect to the optical path difference between thefirst luminous flux and the second luminous flux, so as to determine across spectral density representing spectral information of each pointon the object; and performing back-propagation computation based onFresnel diffraction integral on the cross spectral density, so as todetermine a wavefront of light reflected or scattered at each point onthe object.

The present invention provides a spectrally-resolved three-dimensionalshape measurement device and a spectrally-resolved three-dimensionalshape measurement method capable of measuring the three-dimensionalshape and the spectral information of an object while reducing a timerequired for measuring the object.

The foregoing and other objects, features, aspects and advantages of thepresent invention will become more apparent from the following detaileddescription of the present invention when taken in conjunction with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic configuration diagram of a spectrally-resolvedthree-dimensional shape measurement device according to one embodimentof the present invention.

FIG. 2 is a functional block diagram of a controller.

FIG. 3 is a schematic view of white light fringes obtained by aspectrally-resolved three-dimensional shape measurement device accordingto one embodiment of the present invention.

FIG. 4 is an operation flowchart of a spectrally-resolvedthree-dimensional shape measurement device according to one embodimentof the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

A spectrally-resolved three-dimensional shape measurement deviceaccording to an embodiment of the present invention will now bedescribed with reference to the drawings.

A spectrally-resolved three-dimensional shape measurement deviceaccording to one embodiment of the present invention splits lightreflected or scattered by an object illuminated with white light, intotwo luminous fluxes, by a beam splitting element of an interferometer.The spectrally-resolved three-dimensional shape measurement deviceproduces a difference in wavefront between the two luminous fluxes byreflecting the two luminous fluxes on two reflecting mirrors separatelydisposed and having different curvatures. The spectrally-resolvedthree-dimensional shape measurement device then combines the twoluminous fluxes into one luminous flux again. During the measuringoperation, the spectrally-resolved three-dimensional shape measurementdevice measures the intensity distribution of the combined luminous fluxby an image sensor while moving one of the reflecting mirrors in such adirection as to change the optical path difference between the twoluminous fluxes. The spectrally-resolved three-dimensional shapemeasurement device thus obtains white light fringes including both thethree-dimensional shape information and the spectral information of theobject. Since the spectrally-resolved three-dimensional shapemeasurement device obtains white light fringes by moving only one of thereflecting mirrors in one direction, the device can measure thethree-dimensional shape and the spectral information of the object in areduced time.

FIG. 1 schematically shows a configuration of a spectrally-resolvedthree-dimensional shape measurement device 1 according to one embodimentof the present invention. Spectrally-resolved three-dimensional shapemeasurement device 1 includes an interferometer 2, an image sensor 3,and a controller 4. A condensing optical system (not shown) may furtherbe disposed between interferometer 2 and image sensor 3 to condense aluminous flux traveling from interferometer 2 to image sensor 3.Alternatively, a condensing optical system may be disposed between anobject 10 and interferometer 2 to condense a luminous flux travelingfrom object 10 to interferometer 2.

Interferometer 2 includes a beam splitting element 21, a firstreflecting mirror 22, a second reflecting mirror 23, and a fine movementstage 24. Beam splitting element 21 is formed by a beam splitter or ahalf-silvered mirror, for example. Beam splitting element 21 splitsmeasuring light reflected or scattered by object 10 illuminated withwhite light, into a first luminous flux B1 that travels to firstreflecting mirror 22 and a second luminous flux B2 that travels tosecond reflecting mirror 23. Beam splitting element 21 combines firstluminous flux B1 reflected by first reflecting mirror 22 with secondluminous flux B2 reflected by second reflecting mirror 23 into oneluminous flux, and outputs the combined luminous flux to image sensor 3.

The light source for illuminating object 10 may be of any type and maybe placed in any way. Various types of light sources that emit lighthaving two or more wavelengths may be used, such as natural light, awhite LED, and a plurality of monochromatic LEDs with differentwavelengths. It is preferable that a surface of object 10 be illuminatedwith as uniform an illuminance as possible.

First reflecting mirror 22 is disposed so that its reflection surfacefaces beam splitting element 21 and so that the distance between beamsplitting element 21 and first reflecting mirror 22 is constant. In thepresent embodiment, first reflecting mirror 22 is disposed opposite toobject 10 across beam splitting element 21.

Second reflecting mirror 23 is disposed so that its reflection surfacefaces beam splitting element 21 in the direction orthogonal to the linethat connects object 10 and first reflecting mirror 22 to each other.Second reflecting mirror 23 is disposed on fine movement stage 24movably in the direction away from beam splitting element 21.

First reflecting mirror 22 and second reflecting mirror 23 havedifferent curvatures. For example, first reflecting mirror 22 may be aplane mirror, and second reflecting mirror 23 may be a concave mirror.Both of the two reflecting mirrors may be concave mirrors. This enablesa shorter distance between interferometer 2 and image sensor 3 and candownsize spectrally-resolved three-dimensional shape measurement device1. Alternatively, at least one of the reflecting mirrors may be a convexmirror. Thus, first reflecting mirror 22 and second reflecting mirror 23have different reflection surface curvatures. Therefore, firstreflecting mirror 22 and second reflecting mirror 23 differentlymodulate the wavefronts of luminous flux B1 and luminous flux B2,respectively, when reflecting them. When the two wavefronts aresuperimposed, white light interference occurs according to thedifference in wavefront between luminous flux B1 and luminous flux B2and according to the optical path difference between luminous flux B1and luminous flux B2. Preferably first reflecting mirror 22 and secondreflecting mirror 23 are disposed so that beam splitting element 21turns the optical axis of first reflecting mirror 22 by 90 degrees tocoincide with the optical axis of second reflecting mirror 23. Thisreduces the amount of computation for determining the three-dimensionalshape information and the spectral information of object 10 from whitelight fringes represented by image signals generated by image sensor 3.

Fine movement stage 24 is formed by a piezo stage, for example. On finemovement stage 24, second reflecting mirror 23 is placed. Fine movementstage 24 is connected to controller 4. In response to a control signalfrom controller 4, fine movement stage 24 causes second reflectingmirror 23 placed on fine movement stage 24 to move in the direction awayfrom beam splitting element 21, i.e., in the optical axis direction ofsecond reflecting mirror 23. Movement of fine movement stage 24 enablesadjustment of the distance between second reflecting mirror 23 and beamsplitting element 21. As described above, beam splitting element 21 andfirst reflecting mirror 22 are fixedly disposed at a constant distance.By adjusting the distance between second reflecting mirror 23 and beamsplitting element 21, interferometer 2 can produce a predeterminedoptical path difference between luminous flux B1 and luminous flux B2.

Hereinafter, a coordinate system is defined for convenience in which:the direction parallel to the plane where beam splitting element 21,first reflecting mirror 22, and second reflecting mirror 23 are disposedand along which luminous flux B2 travels to second reflecting mirror 23is an x-axis; a direction orthogonal to the plane is a y-axis; and thedirection parallel to the plane and along which luminous flux B1 travelsto first reflecting mirror 22 is a z-axis. In this coordinate system,the origin (0,0,0) is set on the optical axis of first reflecting mirror22 near object 10.

Image sensor 3 includes two-dimensionally arrayed solid state imagesensing devices, such as CCD or CMOS devices. During the measuringoperation in spectrally-resolved three-dimensional shape measurementdevice 1, image sensor 3 receives a luminous flux obtained by combiningluminous flux B1 reflected by first reflecting mirror 22 and luminousflux B2 reflected by second reflecting mirror 23. Image sensor 3generates an image signal indicating a pixel value of each pixelaccording to the intensity of the received light at the pixel.Specifically, during the measuring operation, image sensor 3 generates aplurality of image signals representing the intensity distribution of aluminous flux obtained by combining luminous flux B1 and luminous fluxB2. Different images correspond to different optical path differencesbetween luminous flux B1 and luminous flux B2. Image sensor 3 isconnected to controller 4. Each time image sensor 3 generates an imagesignal, image sensor 3 outputs the image signal to controller 4. Forexample, image sensor 3 generates about 100 to 1000 images during onemeasuring operation.

Controller 4 is formed by a so-called computer. Controller 4 controlsthe overall spectrally-resolved three-dimensional shape measurementdevice 1. Based on images obtained from image sensor 3, controller 4regenerates the wavefront from each point on object 10, namely, thespectral information of each point on object 10 and thethree-dimensional shape information of object 10.

FIG. 2 shows a functional block diagram of controller 4. As shown inFIG. 2, controller 4 includes: a storage unit 41 including at least oneof a nonvolatile or volatile semiconductor memory, a magnetic disk, anoptical disk, and a reader of them; a communication unit 42 including aninterface circuit configured in accordance with communication standards(e.g. RS232C, Universal Serial Bus, and Ethernet (registeredtrademark)), and software (e.g. a device driver); and a control unit 43including one or more processor, such as a CPU and a numerical valuecomputation processor, and a peripheral circuit of the processor.

Control unit 43 controls fine movement stage 24 by sending a controlsignal via communication unit 42, so as to move second reflecting mirror23 in the x-axis direction and change the optical path differencebetween luminous flux B1 and luminous flux B2. During the measuringoperation, control unit 43 changes the optical path difference by anamount such that white light fringes can be obtained over the range ofwavelength for which regeneration of spectral information of object 10is to be performed. For example, control unit 43 changes the opticalpath difference within a range corresponding to two or three times theupper limit of the range of wavelength and including the optical pathdifference of 0.

Control unit 43 determines the three-dimensional shape information andthe spectral information of object 10 from white light fringesrepresented by a plurality of image signals received from image sensor3.

Hereinafter, the principle for measuring the three-dimensional shape andthe spectral information of object 10 by spectrally-resolvedthree-dimensional shape measurement device 1 is described.

Function R (x,y) representing the phase modulation on a light wavecaused by a spherical mirror having focal length f is expressed by thefollowing equation:

$\begin{matrix}\begin{matrix}{{R\left( {x,y} \right)} = {\exp\left\lbrack {{- \frac{ik}{2\; f}}\left( {x^{2} + y^{2}} \right)} \right\rbrack}} \\{= {Q_{xy}\left( {- \frac{1}{f}} \right)}}\end{matrix} & (1)\end{matrix}$where k denotes a wave number, (x,y) denotes a position of thereflection surface of the spherical mirror in the x-axis direction andthe y-axis direction. If the spherical mirror has a positive power(i.e., the spherical mirror is a concave mirror), focal length f is apositive value.

For example, the distance between a point on the optical axis of firstreflecting mirror 22 and the origin is denoted by d₀, and the distancebetween a point on the optical axis of first reflecting mirror 22 andimage sensor 3 is denoted by d₁. It is assumed that second reflectingmirror 23 moves by distance Z/2 away from beam splitting element 21 inthe x direction, from the position at which the optical path differencebetween luminous flux B1 and luminous flux B2 is 0 to the position atwhich the optical path length difference is Z. In this case, luminousflux B1 emitted from point r_(s)=(x_(s),y_(s),z_(s)) on object 10propagates by distance (d₀−z_(s)) to be modulated by first reflectingmirror 22, and further propagates by distance d₁ to be sensed at imagesensor 3. Luminous flux B2 emitted from point r_(s) propagates bydistance (d₀−z_(s)+Z/2) to be modulated by second reflecting mirror 23,and further propagates by distance (d₁+Z/2) to be sensed at image sensor3. Accordingly, the light wave corresponding to luminous flux B1 and thelight wave corresponding to luminous flux B2 on image sensor 3 areexpressed by the following equations, with no consideration for aquadratic phase factor for the position of point r_(s) that is notrelated to regeneration of a three-dimensional image:

$\begin{matrix}{{U_{1}\left( {\rho,\omega} \right)} = {A\frac{f_{1}}{{d_{1}f_{1}} + {\left( {d_{0} - z_{s}} \right)f_{1}} - \left( {d_{0} - z_{s}} \right)}{\exp\left\lbrack {{ik}\left( {d_{0} + d_{1} - z_{s}} \right)} \right\rbrack} \times {\exp\left\lbrack {\frac{ik}{2}\frac{f_{1} - \left( {d_{0} - z_{s}} \right)}{{d_{1}f_{1}} + {\left( {d_{0} - z_{s}} \right)f_{1}} - {\left( {d_{0} - z_{s}} \right)d_{1}}}\left\{ {\left( {X - {\frac{f_{1}}{f_{1} - \left( {d_{0} - z_{s}} \right)}x_{s}}} \right)^{2} + \left( {Y - {\frac{f_{1}}{f_{1} - \left( {d_{0} - z_{s}} \right)}y_{s}}} \right)^{2}} \right\}} \right\rbrack}}} & (2) \\{{U_{2}\left( {\rho_{is},\omega} \right)} = {A\frac{f_{2}}{{d_{1}f_{2}} + {\left( {d_{0} - z_{s}} \right)f_{2}} - \left( {d_{0} - z_{s}} \right)}{\exp\left\lbrack {{ik}\left( {d_{0} + d_{1} - z_{s}} \right)} \right\rbrack} \times {\exp\left\lbrack {\frac{ik}{2}\frac{f_{2} - \left( {d_{0} - z_{s}} \right)}{{d_{1}f_{2}} + {\left( {d_{0} - z_{s}} \right)f_{2}} - {\left( {d_{0} - z_{s}} \right)d_{1}}}\left\{ {\left( {X - {\frac{f_{2}}{f_{2} - \left( {d_{0} - z_{s}} \right)}x_{s}}} \right)^{2} + \left( {Y - {\frac{f_{2}}{f_{2} - \left( {d_{0} - z_{s}} \right)}y_{s}}} \right)^{2}} \right\}} \right\rbrack}}} & (3)\end{matrix}$where ρ_(is)=(X,Y) denotes coordinates in a real space on image sensor3; ρ=(X,Y,Z)=(ρ_(is),Z) denotes a position vector representing theposition after a movement by distance Z in the x direction from thesensing surface (Z=0) of image sensor 3; f₁ and f₂ respectively denotethe focal length of first reflecting mirror 22 and the focal length ofsecond reflecting mirror 23; ω denotes a frequency according towavelength λ of the light wave. That is, ω=ck=c/λ holds, where c denotesthe velocity of light and k denotes a wave number.

Interference fringes (volume interferogram) I_(p) (ρ,ω) recorded by thelight emitted from a monochromatic light source at position r_(s) andpropagating via interferometer 2 are expressed by the followingequation.

$\begin{matrix}\begin{matrix}{{I_{p}\left( {\rho,\omega} \right)} = \left\langle {{{U_{1}\left( {\rho,\omega} \right)} + {U_{2}\left( {\rho_{is},\omega} \right)}}}^{2} \right\rangle} \\{= \begin{matrix}{\left\langle {{U_{1}\left( {\rho,\omega} \right)}}^{2} \right\rangle + \left\langle {{U_{2}\left( {\rho_{is},\omega} \right)}}^{2} \right\rangle +} \\{\left\langle {U_{1}^{*}\left( {\rho,\omega} \right){U_{2}\left( {\rho_{is},\omega} \right)}} \right\rangle + \left\langle {{{U_{1}\left( {\rho,\omega} \right)}{U_{2}^{*}\left( {\rho_{is},\omega} \right)}}} \right\rangle}\end{matrix}}\end{matrix} & (4)\end{matrix}$

Accordingly, cross spectral density W_(s) (ρ,r_(s),ω) of the opticalfield of interference fringes recorded by the light emitted from themonochromatic light source at position r_(s) and propagating viainterferometer 2 is defined, based on the equations (2) to (4), as thefollowing equations:

$\begin{matrix}\begin{matrix}\begin{matrix}{{W_{s}\left( {\rho,r_{s},\omega} \right)} = \left\langle {{{U_{1}^{*}\left( {\rho,\omega} \right)}{U_{2}\left( {\rho_{is},\omega} \right)}}} \right\rangle} \\{= {{\exp({ikZ})}\exp\left\{ {\frac{ik}{2\;{\gamma\left( z_{s} \right)}}\left\lbrack {\left( {X - {mx}_{s}} \right)^{2} + \left( {Y - {my}_{s}} \right)^{2}} \right\rbrack} \right\}}}\end{matrix} \\{where} \\{{\gamma\left( z_{s} \right)} = \frac{\begin{matrix}{{\left\{ {{f_{1}f_{2}} - {\left( {f_{1} + f_{2}} \right)d_{1}} + d_{1}^{2}} \right\}\left( {d_{0} - z_{z}} \right)^{2}} +} \\{{\left\{ {{2\; f_{1}f_{2}d_{1}} - {\left( {f_{1} + f_{2}} \right)d_{1}^{2}}} \right\}\left( {d_{0} - z_{s}} \right)} + {f_{1}f_{2}d_{1}^{2}}}\end{matrix}}{\left( {d_{0} - z_{s}} \right)^{2}\left( {f_{2} - f_{1}} \right)}} \\{m = {- \frac{d_{1}}{d_{0} - z_{s}}}}\end{matrix} & (5)\end{matrix}$where γ (z_(s)) denotes a curvature radius of a spherical wave phaserecorded as interference fringes, and m denotes a lateral magnificationof a three-dimensional image of the light source. Solving curvatureradius γ (z_(s)) for z_(s) provides the following equation.

$\begin{matrix}{z_{s} = {d_{0}\frac{\begin{matrix}{{2f_{1}f_{2}d_{1}} - {d_{1}^{2}\left( {f_{1} + f_{2}} \right)} +} \\\sqrt{{d_{1}^{4}\left( {f_{1} + f_{2}} \right)}^{2} + {4f_{1}f_{2}d_{1}^{2}\left\{ {{{\gamma\left( z_{s} \right)}\left( {f_{2} - f_{1}} \right)} - d_{1}^{2}} \right\}}}\end{matrix}}{2\left\{ {{{\gamma\left( z_{s} \right)}\left( {f_{2} - f_{1}} \right)} - {f_{1}f_{2}} + {\left( {f_{1} + f_{2}} \right)d_{1}} - d_{1}^{2}} \right\}}}} & (6)\end{matrix}$Thus, from the value of curvature radius γ (z_(s)), an object valueconverted into a reference coordinate system, namely, a coordinatesystem for point r_(s) on object 10, is determined.

In general, light from each point on object 10 is incoherent with eachother. That is, light from each point interferes only with itself butdoes not interfere with light from the other points. A hologram, whichis a record of white light fringes obtained on image sensor 3,additionally includes the intensity of white light fringes of light fromeach point on object 10. Accordingly, when the distribution of lightfrom each point on object 10 is denoted by S (r_(s),ω), white lightfringes I (ρ) recorded by image signals generated by image sensor 3 areexpressed as the integral of the product of S (r_(s),ω) and interferencefringes I_(p) (ρ,ω) generated by the monochromatic point light sourceexpressed by equation (4), with respect to point r_(s), by the followingequation:

$\begin{matrix}\begin{matrix}{{I(\rho)} = {\int{d^{3}r_{s}d\;\omega\;{S\left( {r_{s},\omega} \right)}{I_{p}\left( {\rho,r_{s},\omega} \right)}}}} \\{= {{\Gamma_{1}(\rho)} + {\Gamma_{2}(\rho)} + {\Gamma_{12}(\rho)} + {\Gamma_{12}^{*}(\rho)}}}\end{matrix} & (7)\end{matrix}$where Γ₁ (ρ) and Γ₂ (ρ) denote light intensities of luminous flux B1 andluminous flux B2, respectively, as independent light waves. Spatialcoherence function Γ₁₂ (ρ) is expressed by the following equation:

$\begin{matrix}\begin{matrix}\begin{matrix}{{\Gamma_{12}(\rho)} = \begin{matrix}{\int_{0}^{\infty}{d\;\omega\;{\exp({ikZ})}{\int{d^{3}r_{s}{S\left( {r_{s},\omega} \right)}\exp}}}} \\\left\{ {\frac{ik}{2\;{\gamma\left( z_{s} \right)}}\left\lbrack {\left( {X - {mx}_{s}} \right)^{2} + \left( {Y - {my}_{s}} \right)^{2}} \right\rbrack} \right\}\end{matrix}} \\{\mspace{70mu}{= {c{\int{{dk}\;{\exp({ikZ})}{W\left( {\rho_{is},r_{s},\omega} \right)}}}}}}\end{matrix} \\{{W\left( {\rho_{is},r_{s},\omega} \right)} = {\int{d^{3}r_{s}{S\left( {r_{s},\omega} \right)}\exp\left\{ {\frac{ik}{2\;{\gamma\left( z_{s} \right)}}\left\lbrack {\left( {X - {mx}_{s}} \right)^{2} + \left( {Y - {my}_{s}} \right)^{2}} \right\rbrack} \right\}}}}\end{matrix} & (8)\end{matrix}$where W (ρ_(is),r_(s)ω) denotes a complex hologram representing thespectral information of each point on object 10. Performing Fouriertransformation on spatial coherence function Γ₁₂ (ρ) with respect tooptical path difference Z provides a set of cross spectral density W(ρ_(is),r_(s),ω) for each wavelength.

Since ρ_(is)=(X,Y,0) holds, performing back-propagation computationbased on Fresnel diffraction integral on W (ρ_(is),r_(s),ω) providesregenerated image O (x′,y′,z′,ω) of object 10 at regeneration distancez′ for each wavelength as expressed by the following equation.

$\begin{matrix}{{O\left( {x^{\prime},{y^{\prime}z^{\prime}},\omega} \right)} = {\int{{{dXdYW}\left( {X,Y,r_{s},\omega} \right)}{\exp\left( {- {\frac{ik}{2z^{\prime}}\left\lbrack {\left( {X - x^{\prime}} \right)^{2} + \left( {Y - y^{\prime}} \right)^{2}} \right\rbrack}} \right)}}}} & (9)\end{matrix}$

If regeneration distance z′ is equal to curvature radius γ (z_(s))included in cross spectral density W (ρ_(is),r_(s),ω), a focused imageof object 10 is obtained at coordinates (x′,y′), which are obtained byenlarging coordinates (x_(s),y_(s)) at position z_(s) by magnificationm.

FIG. 3 shows a schematic view of a white light fringe signal acquired byspectrally-resolved three-dimensional shape measurement device 1. Forexample, if object 10 is a point light source on the optical axis offirst reflecting mirror 22, white light fringes 300 arethree-dimensional interference fringes in a Cartesian coordinate systemas shown in FIG. 3, where the axes representing two directions X and Yare orthogonal to each other on image sensor 3 and where the axisrepresenting optical path difference Z between luminous flux B1 andluminous flux B2 is orthogonal to each of the above two axes. Imagesensor 3 generates an image signal representing white light fringes inan XY-plane for each value of optical path difference Z. Therefore,white light fringes 300 are obtained by stacking the image signal foreach Z value. White light fringes 300 form concentric interferencefringes in an XY-plane. In the direction of optical path difference Zbetween luminous fluxes B1 and B2, white light fringes 300 formconcentric interference fringes that depend on the length of Z.

FIG. 4 shows an operation flowchart of spectrally-resolvedthree-dimensional shape measurement device 1 in measuring thethree-dimensional shape and the color of object 10. The operationdescribed hereinafter is controlled by controller 4.

When the measurement starts, control unit 43 of controller 4 acquires animage representing the light intensity distribution generated by imagesensor 3, by sending a control signal to fine movement stage 24 viacommunication unit 42 to vary the optical path difference betweenluminous flux B1 and luminous flux B2 (step S101). Control unit 43stores, in storage unit 41 of controller 4, an image signalcorresponding to the light intensity distribution received from imagesensor 3, with the image signal being associated with the optical pathdifference between luminous flux B1 and luminous flux B2 (step S102).Control unit 43 determines whether or not the image signal has beenobtained over the entire range of a predetermined optical pathdifference (step S103). When the image signal has not been obtained overthe entire range of the optical path difference, control unit 43 returnsthe control to step S101, controls fine movement stage 24 to change theoptical path difference, and repeats steps S101 to S103.

When the image signal has been obtained over the entire range of thepredetermined optical path difference at step S103, control unit 43performs Fourier transformation, for each corresponding pixel, on awhite light fringe signal represented by a plurality of image signalsstored in storage unit 41, with respect to the optical path differencebetween luminous fluxes B1 and B2, in accordance with the aboveequations (6) and (7), thus determining cross spectral density W(ρ_(is),ω) (step S104). Control unit 43 performs back-propagationcomputation based on Fresnel diffraction integral on the determinedcross spectral density W (ρ_(is),ω) in accordance with equation (7),thus determining a regenerated wavefront from each point on object 10(step S105). Controller 4 then ends the process.

As described above, a spectrally-resolved three-dimensional shapemeasurement device according to one embodiment of the present inventionsplits light reflected or scattered by an object illuminated with whitelight into two luminous fluxes, reflects the two luminous fluxes onreflecting mirrors having different curvatures, and combines thereflected two luminous fluxes again. The spectrally-resolvedthree-dimensional shape measurement device records, by using an imagesensor, wavefronts of the combined luminous flux, by varying the opticalpath difference between the two luminous fluxes, thus obtaining whitelight fringes. The spectrally-resolved three-dimensional shapemeasurement device performs, for each pixel, Fourier transformation withrespect to the optical path difference to determine a cross spectraldensity representing the spectral information of each point on theobject. The spectrally-resolved three-dimensional shape measurementdevice further performs back-propagation computation based on Fresneldiffraction integral on the cross spectral density to determine aregenerated wavefront from each point on the object representing thethree-dimensional information of the object. Thus, thespectrally-resolved three-dimensional shape measurement device is simplyrequired to move one of the reflecting mirrors along one axis forobtaining white light fringes. Therefore, the time required formeasuring the three-dimensional shape and the spectral information ofthe object is reduced.

The scope of the present invention is not limited to the aboveembodiment. For example, the two reflecting mirrors included ininterferometer 2 may change positions with each other.

In order to change the optical path difference between luminous fluxesB1 and B2, first reflecting mirror 22 may be moved to change thedistance between first reflecting mirror 22 and beam splitting element21, instead of moving second reflecting mirror 23.

At least one of the two reflecting mirrors may be formed by a reflectivespatial light modulator, such as an LCOS. In this case, controller 4 canchange the curvature of the reflecting mirror by adjusting the voltageto be applied to a liquid crystal layer concentrically around theoptical axis of the reflecting mirror. By adjusting the voltage to beapplied to the liquid crystal layer of the spatial light modulator thatforms the reflecting mirror, controller 4 can control the curvature ofthe reflecting mirror to provide a good signal-to-noise ratio of whitelight fringes.

A spectrally-resolved three-dimensional shape measurement deviceaccording to the above embodiment or its variation may be used forvarious devices that require the spectral information and thethree-dimensional shape information of an object. For example, aspectrally-resolved three-dimensional shape measurement device accordingto the above embodiment or its variation may be used in combination witha microscope. In this case, light from an object may be guided into aninterferometer via an observation optical system of the microscopeincluding an objective lens, for example.

As described above, a person skilled in the art can make variousmodifications in accordance with an embodiment within the scope of thepresent invention.

It should be construed that the embodiments of the present inventiondisclosed herein are by way of example in every respect, not by way oflimitation. The scope of the present invention is defined by the termsof the claims and is intended to include any modification within themeaning and scope equivalent to the terms of the claims.

What is claimed is:
 1. An apparatus for obtaining a three-dimensionalshape and spectral information of an object, the apparatus comprising:an interferometer configured to produce white light fringes based onmeasuring light reflected or scattered by the object illuminated withlight having wavelengths; an image sensor configured to generate animage signal for each pixel, the image signal representing an intensitydistribution of light outputted from the interferometer; and acontroller connected to the image sensor and configured to determine thethree-dimensional shape and the spectral information of the object fromthe image signal, the interferometer including: a beam splitting elementconfigured to split the measuring light into a first luminous flux and asecond luminous flux; a first reflecting mirror having a firstreflection surface arranged for reflecting the first luminous flux tothe beam splitting element, the first reflection surface having a firstcurvature; a second reflecting mirror having a second reflection surfacearranged for reflecting the second luminous flux to the beam splittingelement, the second reflection surface having a second curvaturedifferent from the first curvature; and a movable stage configured tomove the second reflecting mirror in a first direction parallel to astraight line that connects the beam splitting element and the secondreflecting mirror to each other, so as to change a distance between thebeam splitting element and the second reflecting mirror, therebyproducing an optical path difference between the first luminous flux andthe second luminous flux, the controller being configured to: acquire awhite light fringe signal represented by a plurality of the imagesignals generated by the image sensor, while controlling the movablestage to move the second reflecting mirror in the first direction;perform frequency conversion on the white light fringe signal, withrespect to the optical path difference between the first luminous fluxand the second luminous flux, so as to determine a cross spectraldensity representing spectral information of each point on the object;and perform back-propagation computation based on Fresnel diffractionintegral on the cross spectral density, so as to determine a wavefrontof light reflected or scattered at each point on the object.
 2. Theapparatus according to claim 1, wherein both of the first reflectingmirror and the second reflecting mirror are concave mirrors.
 3. A methodadapted for an apparatus, the apparatus comprising: an interferometerconfigured to produce white light fringes with measuring light reflectedor scattered by an object illuminated with light having wavelengths; andan image sensor configured to generate an image signal for each pixel,the image signal representing an intensity distribution of lightoutputted from the interferometer, the interferometer including: a beamsplitting element configured to split the measuring light into a firstluminous flux and a second luminous flux; a first reflecting mirrorhaving a reflection surface arranged for reflecting the first luminousflux to the beam splitting element, the reflection surface having afirst curvature; a second reflecting mirror having a reflection surfacearranged for reflecting the second luminous flux to the beam splittingelement, the reflection surface having a second curvature different fromthe first curvature; and a movable stage configured to move the secondreflecting mirror in a first direction parallel to a straight line thatconnects the beam splitting element and the second reflecting mirror toeach other, so as to change a distance between the beam splittingelement and the second reflecting mirror, thereby producing an opticalpath difference between the first luminous flux and the second luminousflux, the method comprising: acquiring a white light fringe signalrepresented by a plurality of the image signals generated by the imagesensor, while controlling the movable stage to move the secondreflecting mirror in the first direction; performing frequencyconversion on the white light fringe signal, with respect to the opticalpath difference between the first luminous flux and the second luminousflux, so as to determine a cross spectral density representing spectralinformation of each point on the object; and performing back-propagationcomputation based on Fresnel diffraction integral on the cross spectraldensity, so as to determine a wavefront of light reflected or scatteredat each point on the object.